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<div class="title">jama_svd.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef JAMA_SVD_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define JAMA_SVD_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;</div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &quot;tnt_array1d.h&quot;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &quot;tnt_array1d_utils.h&quot;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &quot;tnt_array2d.h&quot;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#include &quot;tnt_array2d_utils.h&quot;</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#include &quot;tnt_math_utils.h&quot;</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// for min(), max() below</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// for abs() below</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">using namespace </span>TNT;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">using namespace </span>std;</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">namespace </span>JAMA</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;{</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00039"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html">   39</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_j_a_m_a_1_1_s_v_d.html">SVD</a> </div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;{</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> U, V;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> s;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        <span class="keywordtype">int</span> m, n;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html#a4aa25bafe4952f526a18c5aabcb3827e">   50</a></span>&#160;   <a class="code" href="class_j_a_m_a_1_1_s_v_d.html#a4aa25bafe4952f526a18c5aabcb3827e">SVD</a> (<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;Arg) {</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;      m = Arg.<a class="code" href="class_t_n_t_1_1_array2_d.html#a3997cd7973cd903cc46c0bd7abde03c0">dim1</a>();</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;      n = Arg.<a class="code" href="class_t_n_t_1_1_array2_d.html#a6efd5ac98f02bb42340be1d5cbf4c9c1">dim2</a>();</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;      <span class="keywordtype">int</span> nu = min(m,n);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;      s = <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a>(min(m+1,n)); </div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;          <span class="comment">//s = Array1D&lt;Real&gt;(m,n); </span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;      U = <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(m, nu, Real(0));</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;      V = <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(n,n);</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;      <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> e(n);</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;      <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> work(m);</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;          <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> A(Arg.<a class="code" href="class_t_n_t_1_1_array2_d.html#a475f33af47a33135fde05d1e01fdf0c3">copy</a>());</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;      <span class="keywordtype">int</span> wantu = 1;                                    <span class="comment">/* boolean */</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;      <span class="keywordtype">int</span> wantv = 1;                                    <span class="comment">/* boolean */</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;          <span class="keywordtype">int</span> i=0, j=0, k=0;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;      <span class="comment">// Reduce A to bidiagonal form, storing the diagonal elements</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;      <span class="comment">// in s and the super-diagonal elements in e.</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;      <span class="keywordtype">int</span> nct = min(m-1,n);</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;      <span class="keywordtype">int</span> nrt = max(0,min(n-2,m));</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;      <span class="keywordflow">for</span> (k = 0; k &lt; max(nct,nrt); k++) {</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;         <span class="keywordflow">if</span> (k &lt; nct) {</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            <span class="comment">// Compute the transformation for the k-th column and</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;            <span class="comment">// place the k-th diagonal in s[k].</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;            <span class="comment">// Compute 2-norm of k-th column without under/overflow.</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;            s[k] = 0;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            <span class="keywordflow">for</span> (i = k; i &lt; m; i++) {</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;               s[k] = <a class="code" href="namespace_t_n_t.html#ae102d1c8992a4fea1cc1b2efeabfcc66">hypot</a>(s[k],A[i][k]);</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;            }</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;            <span class="keywordflow">if</span> (s[k] != 0.0) {</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;               <span class="keywordflow">if</span> (A[k][k] &lt; 0.0) {</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;                  s[k] = -s[k];</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;               }</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;               <span class="keywordflow">for</span> (i = k; i &lt; m; i++) {</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;                  A[i][k] /= s[k];</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;               }</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;               A[k][k] += 1.0;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;            }</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;            s[k] = -s[k];</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;         }</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;         <span class="keywordflow">for</span> (j = k+1; j &lt; n; j++) {</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;            <span class="keywordflow">if</span> ((k &lt; nct) &amp;&amp; (s[k] != 0.0))  {</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            <span class="comment">// Apply the transformation.</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;               Real t(0.0);</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;               <span class="keywordflow">for</span> (i = k; i &lt; m; i++) {</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;                  t += A[i][k]*A[i][j];</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;               }</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;               t = -t/A[k][k];</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;               <span class="keywordflow">for</span> (i = k; i &lt; m; i++) {</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                  A[i][j] += t*A[i][k];</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;               }</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;            }</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;            <span class="comment">// Place the k-th row of A into e for the</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;            <span class="comment">// subsequent calculation of the row transformation.</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            e[j] = A[k][j];</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;         }</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;         <span class="keywordflow">if</span> (wantu &amp; (k &lt; nct)) {</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;            <span class="comment">// Place the transformation in U for subsequent back</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;            <span class="comment">// multiplication.</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;            <span class="keywordflow">for</span> (i = k; i &lt; m; i++) {</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;               U[i][k] = A[i][k];</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;            }</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;         }</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;         <span class="keywordflow">if</span> (k &lt; nrt) {</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;            <span class="comment">// Compute the k-th row transformation and place the</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;            <span class="comment">// k-th super-diagonal in e[k].</span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;            <span class="comment">// Compute 2-norm without under/overflow.</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;            e[k] = 0;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;            <span class="keywordflow">for</span> (i = k+1; i &lt; n; i++) {</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;               e[k] = <a class="code" href="namespace_t_n_t.html#ae102d1c8992a4fea1cc1b2efeabfcc66">hypot</a>(e[k],e[i]);</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;            }</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;            <span class="keywordflow">if</span> (e[k] != 0.0) {</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;               <span class="keywordflow">if</span> (e[k+1] &lt; 0.0) {</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;                  e[k] = -e[k];</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;               }</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;               <span class="keywordflow">for</span> (i = k+1; i &lt; n; i++) {</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;                  e[i] /= e[k];</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;               }</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;               e[k+1] += 1.0;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;            }</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;            e[k] = -e[k];</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;            <span class="keywordflow">if</span> ((k+1 &lt; m) &amp; (e[k] != 0.0)) {</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;            <span class="comment">// Apply the transformation.</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;               <span class="keywordflow">for</span> (i = k+1; i &lt; m; i++) {</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;                  work[i] = 0.0;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;               }</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;               <span class="keywordflow">for</span> (j = k+1; j &lt; n; j++) {</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;                  <span class="keywordflow">for</span> (i = k+1; i &lt; m; i++) {</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;                     work[i] += e[j]*A[i][j];</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;                  }</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;               }</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;               <span class="keywordflow">for</span> (j = k+1; j &lt; n; j++) {</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;                  Real t(-e[j]/e[k+1]);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;                  <span class="keywordflow">for</span> (i = k+1; i &lt; m; i++) {</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;                     A[i][j] += t*work[i];</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;                  }</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;               }</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;            }</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;            <span class="keywordflow">if</span> (wantv) {</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;            <span class="comment">// Place the transformation in V for subsequent</span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;            <span class="comment">// back multiplication.</span></div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;               <span class="keywordflow">for</span> (i = k+1; i &lt; n; i++) {</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;                  V[i][k] = e[i];</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;               }</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            }</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;         }</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;      }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;      <span class="comment">// Set up the final bidiagonal matrix or order p.</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;      <span class="keywordtype">int</span> p = min(n,m+1);</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;      <span class="comment">//int p = m;</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;          <span class="keywordflow">if</span> (nct &lt; n) {</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;         s[nct] = A[nct][nct];</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;      }</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;      <span class="keywordflow">if</span> (m &lt; p) {</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;         s[p-1] = 0.0;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;      }</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      <span class="keywordflow">if</span> (nrt+1 &lt; p) {</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;         e[nrt] = A[nrt][p-1];</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;      }</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;      e[p-1] = 0.0;</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;      <span class="comment">// If required, generate U.</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;      <span class="keywordflow">if</span> (wantu) {</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;         <span class="keywordflow">for</span> (j = nct; j &lt; nu; j++) {</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;            <span class="keywordflow">for</span> (i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;               U[i][j] = 0.0;</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;            }</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;            U[j][j] = 1.0;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;         }</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;         <span class="keywordflow">for</span> (k = nct-1; k &gt;= 0; k--) {</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;            <span class="keywordflow">if</span> (s[k] != 0.0) {</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;               <span class="keywordflow">for</span> (j = k+1; j &lt; nu; j++) {</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;                  Real t(0.0);</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;                  <span class="keywordflow">for</span> (i = k; i &lt; m; i++) {</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;                     t += U[i][k]*U[i][j];</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                  }</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;                  t = -t/U[k][k];</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;                  <span class="keywordflow">for</span> (i = k; i &lt; m; i++) {</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;                     U[i][j] += t*U[i][k];</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;                  }</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;               }</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;               <span class="keywordflow">for</span> (i = k; i &lt; m; i++ ) {</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;                  U[i][k] = -U[i][k];</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;               }</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;               U[k][k] = 1.0 + U[k][k];</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;               <span class="keywordflow">for</span> (i = 0; i &lt; k-1; i++) {</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;                  U[i][k] = 0.0;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;               }</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;               <span class="keywordflow">for</span> (i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;                  U[i][k] = 0.0;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;               }</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;               U[k][k] = 1.0;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;            }</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;         }</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;      }</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;      <span class="comment">// If required, generate V.</span></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;      <span class="keywordflow">if</span> (wantv) {</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;         <span class="keywordflow">for</span> (k = n-1; k &gt;= 0; k--) {</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;            <span class="keywordflow">if</span> ((k &lt; nrt) &amp; (e[k] != 0.0)) {</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;               <span class="keywordflow">for</span> (j = k+1; j &lt; nu; j++) {</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;                  Real t(0.0);</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;                  <span class="keywordflow">for</span> (i = k+1; i &lt; n; i++) {</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;                     t += V[i][k]*V[i][j];</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;                  }</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;                  t = -t/V[k+1][k];</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;                  <span class="keywordflow">for</span> (i = k+1; i &lt; n; i++) {</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;                     V[i][j] += t*V[i][k];</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;                  }</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;               }</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;            }</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;            <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;               V[i][k] = 0.0;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;            }</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;            V[k][k] = 1.0;</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;         }</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;      }</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;      <span class="comment">// Main iteration loop for the singular values.</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;      <span class="keywordtype">int</span> pp = p-1;</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;      <span class="keywordtype">int</span> iter = 0;</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;      Real eps(pow(2.0,-52.0));</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;      <span class="keywordflow">while</span> (p &gt; 0) {</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;         <span class="keywordtype">int</span> k=0;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;                 <span class="keywordtype">int</span> kase=0;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;         <span class="comment">// Here is where a test for too many iterations would go.</span></div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;         <span class="comment">// This section of the program inspects for</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;         <span class="comment">// negligible elements in the s and e arrays.  On</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;         <span class="comment">// completion the variables kase and k are set as follows.</span></div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;         <span class="comment">// kase = 1     if s(p) and e[k-1] are negligible and k&lt;p</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;         <span class="comment">// kase = 2     if s(k) is negligible and k&lt;p</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;         <span class="comment">// kase = 3     if e[k-1] is negligible, k&lt;p, and</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;         <span class="comment">//              s(k), ..., s(p) are not negligible (qr step).</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;         <span class="comment">// kase = 4     if e(p-1) is negligible (convergence).</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;         <span class="keywordflow">for</span> (k = p-2; k &gt;= -1; k--) {</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;            <span class="keywordflow">if</span> (k == -1) {</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;               <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;            }</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;            <span class="keywordflow">if</span> (abs(e[k]) &lt;= eps*(abs(s[k]) + abs(s[k+1]))) {</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;               e[k] = 0.0;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;               <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;            }</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;         }</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;         <span class="keywordflow">if</span> (k == p-2) {</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;            kase = 4;</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;         } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;            <span class="keywordtype">int</span> ks;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;            <span class="keywordflow">for</span> (ks = p-1; ks &gt;= k; ks--) {</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;               <span class="keywordflow">if</span> (ks == k) {</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;                  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;               }</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;               Real t( (ks != p ? abs(e[ks]) : 0.) + </div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;                          (ks != k+1 ? abs(e[ks-1]) : 0.));</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;               <span class="keywordflow">if</span> (abs(s[ks]) &lt;= eps*t)  {</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;                  s[ks] = 0.0;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;               }</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;            }</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;            <span class="keywordflow">if</span> (ks == k) {</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;               kase = 3;</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (ks == p-1) {</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;               kase = 1;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;               kase = 2;</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;               k = ks;</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;            }</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;         }</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;         k++;</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;         <span class="comment">// Perform the task indicated by kase.</span></div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;         <span class="keywordflow">switch</span> (kase) {</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;            <span class="comment">// Deflate negligible s(p).</span></div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;            <span class="keywordflow">case</span> 1: {</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;               Real f(e[p-2]);</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;               e[p-2] = 0.0;</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;               <span class="keywordflow">for</span> (j = p-2; j &gt;= k; j--) {</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;                  Real t( <a class="code" href="namespace_t_n_t.html#ae102d1c8992a4fea1cc1b2efeabfcc66">hypot</a>(s[j],f));</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;                  Real cs(s[j]/t);</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;                  Real sn(f/t);</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;                  s[j] = t;</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;                  <span class="keywordflow">if</span> (j != k) {</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;                     f = -sn*e[j-1];</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;                     e[j-1] = cs*e[j-1];</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;                  }</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;                  <span class="keywordflow">if</span> (wantv) {</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;                     <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;                        t = cs*V[i][j] + sn*V[i][p-1];</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;                        V[i][p-1] = -sn*V[i][j] + cs*V[i][p-1];</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;                        V[i][j] = t;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;                     }</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;                  }</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;               }</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;            }</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;            <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;            <span class="comment">// Split at negligible s(k).</span></div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;            <span class="keywordflow">case</span> 2: {</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;               Real f(e[k-1]);</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;               e[k-1] = 0.0;</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;               <span class="keywordflow">for</span> (j = k; j &lt; p; j++) {</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;                  Real t(<a class="code" href="namespace_t_n_t.html#ae102d1c8992a4fea1cc1b2efeabfcc66">hypot</a>(s[j],f));</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;                  Real cs( s[j]/t);</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;                  Real sn(f/t);</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;                  s[j] = t;</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;                  f = -sn*e[j];</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;                  e[j] = cs*e[j];</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;                  <span class="keywordflow">if</span> (wantu) {</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;                     <span class="keywordflow">for</span> (i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;                        t = cs*U[i][j] + sn*U[i][k-1];</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;                        U[i][k-1] = -sn*U[i][j] + cs*U[i][k-1];</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;                        U[i][j] = t;</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;                     }</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;                  }</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;               }</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;            }</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;            <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;            <span class="comment">// Perform one qr step.</span></div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;            <span class="keywordflow">case</span> 3: {</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;               <span class="comment">// Calculate the shift.</span></div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;   </div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;               Real scale = max(max(max(max(</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;                       abs(s[p-1]),abs(s[p-2])),abs(e[p-2])), </div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;                       abs(s[k])),abs(e[k]));</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;               Real sp = s[p-1]/scale;</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;               Real spm1 = s[p-2]/scale;</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;               Real epm1 = e[p-2]/scale;</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;               Real sk = s[k]/scale;</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;               Real ek = e[k]/scale;</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;               Real b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)/2.0;</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;               Real c = (sp*epm1)*(sp*epm1);</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;               Real shift = 0.0;</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;               <span class="keywordflow">if</span> ((b != 0.0) || (c != 0.0)) {</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;                  shift = sqrt(b*b + c);</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;                  <span class="keywordflow">if</span> (b &lt; 0.0) {</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;                     shift = -shift;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;                  }</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;                  shift = c/(b + shift);</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;               }</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;               Real f = (sk + sp)*(sk - sp) + shift;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;               Real g = sk*ek;</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;   </div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;               <span class="comment">// Chase zeros.</span></div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;   </div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;               <span class="keywordflow">for</span> (j = k; j &lt; p-1; j++) {</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;                  Real t = <a class="code" href="namespace_t_n_t.html#ae102d1c8992a4fea1cc1b2efeabfcc66">hypot</a>(f,g);</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;                  Real cs = f/t;</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;                  Real sn = g/t;</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;                  <span class="keywordflow">if</span> (j != k) {</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;                     e[j-1] = t;</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;                  }</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;                  f = cs*s[j] + sn*e[j];</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;                  e[j] = cs*e[j] - sn*s[j];</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;                  g = sn*s[j+1];</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;                  s[j+1] = cs*s[j+1];</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;                  <span class="keywordflow">if</span> (wantv) {</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;                     <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;                        t = cs*V[i][j] + sn*V[i][j+1];</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;                        V[i][j+1] = -sn*V[i][j] + cs*V[i][j+1];</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;                        V[i][j] = t;</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;                     }</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;                  }</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;                  t = <a class="code" href="namespace_t_n_t.html#ae102d1c8992a4fea1cc1b2efeabfcc66">hypot</a>(f,g);</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;                  cs = f/t;</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;                  sn = g/t;</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;                  s[j] = t;</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;                  f = cs*e[j] + sn*s[j+1];</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;                  s[j+1] = -sn*e[j] + cs*s[j+1];</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;                  g = sn*e[j+1];</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;                  e[j+1] = cs*e[j+1];</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;                  <span class="keywordflow">if</span> (wantu &amp;&amp; (j &lt; m-1)) {</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;                     <span class="keywordflow">for</span> (i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;                        t = cs*U[i][j] + sn*U[i][j+1];</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;                        U[i][j+1] = -sn*U[i][j] + cs*U[i][j+1];</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;                        U[i][j] = t;</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;                     }</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;                  }</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;               }</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;               e[p-2] = f;</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;               iter = iter + 1;</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;            }</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;            <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;            <span class="comment">// Convergence.</span></div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;            <span class="keywordflow">case</span> 4: {</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;               <span class="comment">// Make the singular values positive.</span></div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;   </div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;               <span class="keywordflow">if</span> (s[k] &lt;= 0.0) {</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;                  s[k] = (s[k] &lt; 0.0 ? -s[k] : 0.0);</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;                  <span class="keywordflow">if</span> (wantv) {</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;                     <span class="keywordflow">for</span> (i = 0; i &lt;= pp; i++) {</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;                        V[i][k] = -V[i][k];</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;                     }</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;                  }</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;               }</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;   </div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;               <span class="comment">// Order the singular values.</span></div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;   </div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;               <span class="keywordflow">while</span> (k &lt; pp) {</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;                  <span class="keywordflow">if</span> (s[k] &gt;= s[k+1]) {</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;                     <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;                  }</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;                  Real t = s[k];</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;                  s[k] = s[k+1];</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;                  s[k+1] = t;</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;                  <span class="keywordflow">if</span> (wantv &amp;&amp; (k &lt; n-1)) {</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;                     <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;                        t = V[i][k+1]; V[i][k+1] = V[i][k]; V[i][k] = t;</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;                     }</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;                  }</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;                  <span class="keywordflow">if</span> (wantu &amp;&amp; (k &lt; m-1)) {</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;                     <span class="keywordflow">for</span> (i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;                        t = U[i][k+1]; U[i][k+1] = U[i][k]; U[i][k] = t;</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;                     }</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;                  }</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;                  k++;</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;               }</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;               iter = 0;</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;               p--;</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;            }</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;            <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;         }</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;      }</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;   }</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;</div>
<div class="line"><a name="l00468"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html#ae7f5faa245069309abd8b1b630f71ca0">  468</a></span>&#160;   <span class="keywordtype">void</span> getU (<a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;A) </div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;   {</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;         <span class="comment">//int minm = min(m+1,n); // Changed by Piotr</span></div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;         <span class="keywordtype">int</span> minm = m;</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;          A = <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(m, minm);</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;          <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;m; i++)</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=0; j&lt;minm; j++)</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;                        A[i][j] = U[i][j];</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;        </div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;   }</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;   <span class="comment">/* Return the right singular vectors */</span></div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;</div>
<div class="line"><a name="l00482"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html#a16c66d5d97354f8b2ec87a4c603a02d6">  482</a></span>&#160;   <span class="keywordtype">void</span> getV (<a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;A) </div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;   {</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;          A = V;</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;   }</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;</div>
<div class="line"><a name="l00489"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html#afbb53e2a3828bd158a45ea87562e7a08">  489</a></span>&#160;   <span class="keywordtype">void</span> getSingularValues (<a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> &amp;x) </div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;   {</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;      x = s;</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;   }</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;</div>
<div class="line"><a name="l00498"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html#ad25ba091d8385d45bb38e24962cad60a">  498</a></span>&#160;   <span class="keywordtype">void</span> <a class="code" href="class_j_a_m_a_1_1_s_v_d.html#ad25ba091d8385d45bb38e24962cad60a">getS</a> (<a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;A) {</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;          A = <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(n,n);</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;            A[i][j] = 0.0;</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;         }</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;         A[i][i] = s[i];</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;      }</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;   }</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;</div>
<div class="line"><a name="l00510"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html#a67bc975d69b8eaf4c467641f4df6dcf4">  510</a></span>&#160;   Real <a class="code" href="class_j_a_m_a_1_1_s_v_d.html#a67bc975d69b8eaf4c467641f4df6dcf4">norm2</a> () {</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;      <span class="keywordflow">return</span> s[0];</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;   }</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;</div>
<div class="line"><a name="l00516"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html#a70b2e3aaa8720b352d126b30afe7e105">  516</a></span>&#160;   Real <a class="code" href="class_j_a_m_a_1_1_s_v_d.html#a70b2e3aaa8720b352d126b30afe7e105">cond</a> () {</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;      <span class="keywordflow">return</span> s[0]/s[min(m,n)-1];</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;   }</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;</div>
<div class="line"><a name="l00524"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_s_v_d.html#a20aa98558dc53170fd899b474f540bd2">  524</a></span>&#160;   <span class="keywordtype">int</span> rank () </div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;   {</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;      Real eps = pow(2.0,-52.0);</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;      Real tol = max(m,n)*s[0]*eps;</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;      <span class="keywordtype">int</span> r = 0;</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; s.dim(); i++) {</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;         <span class="keywordflow">if</span> (s[i] &gt; tol) {</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;            r++;</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;         }</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;      }</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;      <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;   }</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;};</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;}</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;<span class="preprocessor"></span><span class="comment">// JAMA_SVD_H</span></div>
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